I don't think NG+ complete round 2 should be implemented as I feel Werster's complete the game run may be in vain if that happened. This category wouldn't take away that hard work because GLC Round 2 and round 1 would not be included.
Round 2 is definitely lacking a completion category besides GLC. Obviously it's a slight issue that someone has to own a copy with round 1 completed. But honestly, no one should be playing round 2 without having completed round 1 anyway in my opinion. But it only takes beating it once.
'IF' this were to be implemented, it could be considered to put a rule where you must do PRIME cup and POKE cup in order if the NG+ aspect is not a desirable feature. That way it stays sort of a more traditional completion like complete round 1, because obviously on a fresh cartridge OR fresh round 2, only pokeball, pika, and petit are available. Having the NG+ aspect would allow ANY order of the tournaments. I could go either way myself. Just some thoughts =)